Theorem rgenw

Description: Generalization rule for restricted quantification. (Contributed by NM, 18-Jun-2014)

	Ref	Expression
Hypothesis	rgenw.1	⊢ 𝜑
Assertion	rgenw	⊢ ∀ 𝑥 ∈ 𝐴 𝜑

Proof

Step	Hyp	Ref	Expression
1		rgenw.1	⊢ 𝜑
2	1	a1i	⊢ ( 𝑥 ∈ 𝐴 → 𝜑 )
3	2	rgen	⊢ ∀ 𝑥 ∈ 𝐴 𝜑